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Milgromian dynamics (MD or MOND) uniquely predicts motion in a galaxy fromthe distribution of its stars and gas in a remarkable agreement withobservations so far. In the solar system, MD predicts the existence of somepossibly non-negligible dynamical effects, which can be used to constrain thefreedom in MD theories. Known extreme trans-Neptunian objects (ETNOs) havetheir argument of perihelion, longitude of ascending node, and inclinationdistributed in highly non-uniform fashion; ETNOs are bodies with periheliondistances greater than the orbit of Neptune and with semimajor axes greaterthan 150 au and less than $\sim1500$ au. It is as if these bodies have beensystematically perturbed by some external force. We investigated a hypothesisthat the puzzling orbital characteristics of ETNOs are a consequence of MD. Weset up a dynamical model of the solar system incorporating the external fieldeffect (EFE), which is anticipated to be the dominant effect of MD in the ETNOsregion. We used constraints available on the strength of EFE coming from radiotracking of the Cassini spacecraft. We performed several numerical experiments,concentrating on the long-term orbital evolution of primordial (randomised)ETNOs in MD. The EFE could produce distinct non-uniform distributions of theorbital elements of ETNOs that are related to the orientation of an orbit inspace. If we demand that EFE is solely responsible for the detachment of Sednaand 2012 VP$_{113}$, then these distributions are at odds with the currentlyobserved statistics on ETNOs unless the EFE quadrupole strength parameter$Q_{2}$ has values that are unlikely (with probability < 1$\%$) in light of theCassini data.

Towards an explanation of orbits in the extreme trans-Neptunian region: The effect of Milgromian dynamics